-
Notifications
You must be signed in to change notification settings - Fork 192
/
IntMod.cpp
1274 lines (1011 loc) · 28 KB
/
IntMod.cpp
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
/*
* This file is part of the BSGS distribution (https://github.com/JeanLucPons/VanitySearch).
* Copyright (c) 2020 Jean Luc PONS.
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, version 3.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#include "Int.h"
#include <emmintrin.h>
#include <string.h>
#define MAX(x,y) (((x)>(y))?(x):(y))
#define MIN(x,y) (((x)<(y))?(x):(y))
static Int _P; // Field characteristic
static Int _R; // Montgomery multiplication R
static Int _R2; // Montgomery multiplication R2
static Int _R3; // Montgomery multiplication R3
static Int _R4; // Montgomery multiplication R4
static int32_t Msize; // Montgomery mult size
static uint32_t MM32; // 32bits lsb negative inverse of P
static uint64_t MM64; // 64bits lsb negative inverse of P
#define MSK62 0x3FFFFFFFFFFFFFFF
extern Int _ONE;
// ------------------------------------------------
void Int::ModAdd(Int *a) {
Int p;
Add(a);
p.Sub(this,&_P);
if(p.IsPositive())
Set(&p);
}
// ------------------------------------------------
void Int::ModAdd(Int *a, Int *b) {
Int p;
Add(a,b);
p.Sub(this,&_P);
if(p.IsPositive())
Set(&p);
}
// ------------------------------------------------
void Int::ModDouble() {
Int p;
Add(this);
p.Sub(this,&_P);
if(p.IsPositive())
Set(&p);
}
// ------------------------------------------------
void Int::ModAdd(uint64_t a) {
Int p;
Add(a);
p.Sub(this,&_P);
if(p.IsPositive())
Set(&p);
}
// ------------------------------------------------
void Int::ModSub(Int *a) {
Sub(a);
if (IsNegative())
Add(&_P);
}
// ------------------------------------------------
void Int::ModSub(uint64_t a) {
Sub(a);
if (IsNegative())
Add(&_P);
}
// ------------------------------------------------
void Int::ModSub(Int *a,Int *b) {
Sub(a,b);
if (IsNegative())
Add(&_P);
}
// ------------------------------------------------
void Int::ModNeg() {
Neg();
Add(&_P);
}
// ------------------------------------------------
// INV256[x] = x^-1 (mod 256)
int64_t INV256[] = {
-0LL,-1LL,-0LL,-235LL,-0LL,-141LL,-0LL,-183LL,-0LL,-57LL,-0LL,-227LL,-0LL,-133LL,-0LL,-239LL,
-0LL,-241LL,-0LL,-91LL,-0LL,-253LL,-0LL,-167LL,-0LL,-41LL,-0LL,-83LL,-0LL,-245LL,-0LL,-223LL,
-0LL,-225LL,-0LL,-203LL,-0LL,-109LL,-0LL,-151LL,-0LL,-25LL,-0LL,-195LL,-0LL,-101LL,-0LL,-207LL,
-0LL,-209LL,-0LL,-59LL,-0LL,-221LL,-0LL,-135LL,-0LL,-9LL,-0LL,-51LL,-0LL,-213LL,-0LL,-191LL,
-0LL,-193LL,-0LL,-171LL,-0LL,-77LL,-0LL,-119LL,-0LL,-249LL,-0LL,-163LL,-0LL,-69LL,-0LL,-175LL,
-0LL,-177LL,-0LL,-27LL,-0LL,-189LL,-0LL,-103LL,-0LL,-233LL,-0LL,-19LL,-0LL,-181LL,-0LL,-159LL,
-0LL,-161LL,-0LL,-139LL,-0LL,-45LL,-0LL,-87LL,-0LL,-217LL,-0LL,-131LL,-0LL,-37LL,-0LL,-143LL,
-0LL,-145LL,-0LL,-251LL,-0LL,-157LL,-0LL,-71LL,-0LL,-201LL,-0LL,-243LL,-0LL,-149LL,-0LL,-127LL,
-0LL,-129LL,-0LL,-107LL,-0LL,-13LL,-0LL,-55LL,-0LL,-185LL,-0LL,-99LL,-0LL,-5LL,-0LL,-111LL,
-0LL,-113LL,-0LL,-219LL,-0LL,-125LL,-0LL,-39LL,-0LL,-169LL,-0LL,-211LL,-0LL,-117LL,-0LL,-95LL,
-0LL,-97LL,-0LL,-75LL,-0LL,-237LL,-0LL,-23LL,-0LL,-153LL,-0LL,-67LL,-0LL,-229LL,-0LL,-79LL,
-0LL,-81LL,-0LL,-187LL,-0LL,-93LL,-0LL,-7LL,-0LL,-137LL,-0LL,-179LL,-0LL,-85LL,-0LL,-63LL,
-0LL,-65LL,-0LL,-43LL,-0LL,-205LL,-0LL,-247LL,-0LL,-121LL,-0LL,-35LL,-0LL,-197LL,-0LL,-47LL,
-0LL,-49LL,-0LL,-155LL,-0LL,-61LL,-0LL,-231LL,-0LL,-105LL,-0LL,-147LL,-0LL,-53LL,-0LL,-31LL,
-0LL,-33LL,-0LL,-11LL,-0LL,-173LL,-0LL,-215LL,-0LL,-89LL,-0LL,-3LL,-0LL,-165LL,-0LL,-15LL,
-0LL,-17LL,-0LL,-123LL,-0LL,-29LL,-0LL,-199LL,-0LL,-73LL,-0LL,-115LL,-0LL,-21LL,-0LL,-255LL, };
void Int::DivStep62(Int* u,Int* v,int64_t* eta,int* pos,int64_t* uu,int64_t* uv,int64_t* vu,int64_t* vv) {
// u' = (uu*u + uv*v) >> bitCount
// v' = (vu*u + vv*v) >> bitCount
// Do not maintain a matrix for r and s, the number of
// 'added P' can be easily calculated
// Performance are measured on a I5-8500 for P=2^256 - 0x1000003D1 (VS2019 compilation)
int bitCount;
uint64_t u0 = u->bits64[0];
uint64_t v0 = v->bits64[0];
#if 0
*uu = 1; *uv = 0;
*vu = 0; *vv = 1;
#define SWAP_ADD(x,y) x+=y;y-=x;
#define SWAP_SUB(x,y) x-=y;y+=x;
// Former divstep62 (using __builtin_ctzll)
// Avg: 632 Kinv/s, Avg number of divstep62: 9.83
bitCount = 62;
int64_t nb0;
__m128i _u;
__m128i _v;
_u.m128i_u64[0] = 1;
_u.m128i_u64[1] = 0;
_v.m128i_u64[0] = 0;
_v.m128i_u64[1] = 1;
while(true) {
int zeros = TZC(v0 | (UINT64_MAX << bitCount));
v0 >>= zeros;
_u = _mm_slli_epi64(_u,(int)zeros);
bitCount -= zeros;
if(bitCount <= 0)
break;
nb0 = (v0 + u0) & 0x3;
if(nb0 == 0) {
_v = _mm_add_epi64(_v,_u);
_u = _mm_sub_epi64(_u,_v);
SWAP_ADD(v0,u0);
} else {
_v = _mm_sub_epi64(_v,_u);
_u = _mm_add_epi64(_u,_v);
SWAP_SUB(v0,u0);
}
}
*uu = _u.m128i_u64[0];
*uv = _u.m128i_u64[1];
*vu = _v.m128i_u64[0];
*vv = _v.m128i_u64[1];
#endif
#if 1
#define SWAP(tmp,x,y) tmp = x; x = y; y = tmp;
// divstep62 var time implementation (Thomas Pornin's method)
// (see https://github.com/pornin/bingcd)
// Avg 780 Kinv/s, Avg number of divstep62: 6.13
// "Make u,v positive" in the macro loop must be enabled
uint64_t uh;
uint64_t vh;
uint64_t w,x;
unsigned char c = 0;
// Extract 64 MSB of u and v
// u and v must be positive
while(*pos>=1 && (u->bits64[*pos] | v->bits64[*pos])==0) (*pos)--;
if(*pos==0) {
uh = u->bits64[0];
vh = v->bits64[0];
} else {
uint64_t s = LZC(u->bits64[*pos] | v->bits64[*pos]);
if(s == 0) {
uh = u->bits64[*pos];
vh = v->bits64[*pos];
} else {
uh = __shiftleft128(u->bits64[*pos-1],u->bits64[*pos],(uint8_t)s);
vh = __shiftleft128(v->bits64[*pos-1],v->bits64[*pos],(uint8_t)s);
}
}
bitCount = 62;
__m128i _u;
__m128i _v;
__m128i _t;
#ifdef WIN64
_u.m128i_u64[0] = 1;
_u.m128i_u64[1] = 0;
_v.m128i_u64[0] = 0;
_v.m128i_u64[1] = 1;
#else
((int64_t *)&_u)[0] = 1;
((int64_t *)&_u)[1] = 0;
((int64_t *)&_v)[0] = 0;
((int64_t *)&_v)[1] = 1;
#endif
while(true) {
// Use a sentinel bit to count zeros only up to bitCount
uint64_t zeros = TZC(v0 | 1ULL << bitCount);
vh >>= zeros;
v0 >>= zeros;
_u = _mm_slli_epi64(_u,(int)zeros);
bitCount -= (int)zeros;
if(bitCount <= 0) {
break;
}
if( vh < uh ) {
SWAP(w,uh,vh);
SWAP(x,u0,v0);
SWAP(_t,_u,_v);
}
vh -= uh;
v0 -= u0;
_v = _mm_sub_epi64(_v,_u);
}
#ifdef WIN64
*uu = _u.m128i_u64[0];
*uv = _u.m128i_u64[1];
*vu = _v.m128i_u64[0];
*vv = _v.m128i_u64[1];
#else
*uu = ((int64_t *)&_u)[0];
*uv = ((int64_t *)&_u)[1];
*vu = ((int64_t *)&_v)[0];
*vv = ((int64_t *)&_v)[1];
#endif
#endif
#if 0
#define SWAP_NEG(tmp,x,y) tmp = x; x = y; y = -tmp;
int64_t m,w,x,y,z;
bitCount = 62;
int64_t limit;
*uu = 1; *uv = 0;
*vu = 0; *vv = 1;
// divstep62 var time implementation by Peter Dettman (based on Bernstein/Yang paper)
// (see https://github.com/bitcoin-core/secp256k1/pull/767)
// Avg: 700 Kinv/s, Avg number of divstep62: 9.00
while(true) {
// Use a sentinel bit to count zeros only up to bitCount
int zeros = TZC(v0 | (1ULL << bitCount));
v0 >>= zeros;
*uu <<= zeros;
*uv <<= zeros;
*eta -= zeros;
bitCount -= zeros;
if(bitCount <= 0) {
break;
}
if(*eta < 0) {
*eta = -*eta;
SWAP_NEG(x,u0,v0);
SWAP_NEG(y,*uu,*vu);
SWAP_NEG(z,*uv,*vv);
}
// Handle up to 6 divstep at once
limit = (*eta + 1) > bitCount ? bitCount : (*eta + 1);
m = (UINT64_MAX >> (64 - limit)) & 63U;
//w = (u0 * v0 * (u0 * u0 - 2)) & m; // w = v0 * -u0^-1 mod 2^6 (1 Newton step => 6bit)
w = (v0 * INV256[u0 & 63U]) & m;
v0 += u0 * w;
*vu += *uu * w;
*vv += *uv * w;
}
#endif
#if 0
// divstep62 constant time implementation by Peter Dettman (based on Bernstein/Yang paper)
// (see https://github.com/bitcoin-core/secp256k1/pull/767)
// Avg: 405 Kinv/s, Avg number of divstep62: 9.00
uint64_t c1,c2,x,y,z;
for(bitCount = 0; bitCount < 62; bitCount++) {
c1 = -(v0 & ((uint64_t)(*eta) >> 63));
x = (u0 ^ v0) & c1;
u0 ^= x; v0 ^= x; v0 ^= c1; v0 -= c1;
y = (*uu ^ *vu) & c1;
*uu ^= y; *vu ^= y; *vu ^= c1; *vu -= c1;
z = (*uv ^ *vv) & c1;
*uv ^= z; *vv ^= z; *vv ^= c1; *vv -= c1;
*eta = (*eta ^ c1) - c1 - 1;
c2 = -(v0 & 1);
v0 += (u0 & c2); v0 >>= 1;
*vu += (*uu & c2); *uu <<= 1;
*vv += (*uv & c2); *uv <<= 1;
}
#endif
}
// ------------------------------------------------
uint64_t totalCount;
void Int::ModInv() {
// Compute modular inverse of this mop _P
// 0 <= this < _P , _P must be odd
// Return 0 if no inverse
// 256bit
//#define XCD 1 // ~97 kOps/s
//#define MONTGOMERY 1 // ~360 kOps/s
#define DRS62 1 // ~780 kOps/s
Int u(&_P);
Int v(this);
Int r((int64_t)0);
Int s((int64_t)1);
#ifdef XCD
Int q, t1, t2, w;
// Classic XCD
bool bIterations = true; // Remember odd/even iterations
while (!u.IsZero()) {
// Step X3. Divide and "Subtract"
q.Set(&v);
q.Div(&u, &t2); // q = u / v, t2 = u % v
w.Mult(&q, &r); // w = q * r
t1.Add(&s, &w); // t1 = s + w
// Swap u,v & r,s
s.Set(&r);
r.Set(&t1);
v.Set(&u);
u.Set(&t2);
bIterations = !bIterations;
}
if (!v.IsOne()) {
CLEAR();
return;
}
if (!bIterations) {
Set(&_P);
Sub(&s); /* inv = n - u1 */
} else {
Set(&s); /* inv = u1 */
}
#endif
#ifdef MONTGOMERY
Int x;
int k = 0;
if(v.IsZero()) {
Set(&v);
return;
}
// Montgomery method
while (v.IsStrictPositive()) {
if (u.IsEven()) {
shiftR(1, u.bits64);
shiftL(1, s.bits64);
} else if (v.IsEven()) {
shiftR(1, v.bits64);
shiftL(1, r.bits64);
} else {
x.Set(&u);
x.Sub(&v);
if (x.IsStrictPositive()) {
shiftR(1, x.bits64);
u.Set(&x);
r.Add(&s);
shiftL(1, s.bits64);
} else {
x.Neg();
shiftR(1, x.bits64);
v.Set(&x);
s.Add(&r);
shiftL(1, r.bits64);
}
}
k++;
}
if (r.IsGreater(&_P))
r.Sub(&_P);
r.Neg();
r.Add(&_P);
// Demontgomerise (divide by 2^k)
uint64_t ML;
uint64_t carryR;
while (k>=64) {
ML = r.bits64[0] * MM64;
imm_umul(_P.bits64,ML,s.bits64);
carryR = r.AddCh(&s,0);
r.ShiftR64Bit();
r.bits64[NB64BLOCK-1] = carryR;
k-=64;
}
if(k>0) {
uint64_t mask = (1ULL << k) - 1;
ML = (r.bits64[0] * MM64) & mask;
imm_umul(_P.bits64,ML,s.bits64);
carryR = r.AddCh(&s,0);
shiftR(k,r.bits64,carryR);
}
if(r.IsGreater(&_P))
r.Sub(&_P);
Set(&r);
#endif
#ifdef DRS62
// Delayed right shift 62bits
Int r0_P;
Int s0_P;
int64_t eta = -1;
int64_t uu,uv,vu,vv;
uint64_t carryS,carryR;
int pos = NB64BLOCK - 1;
while(pos >= 1 && (u.bits64[pos] | v.bits64[pos]) == 0) pos--;
//printf("ModInv(%s)\n",GetBase16().c_str());
while (!v.IsZero()) {
DivStep62(&u,&v,&eta,&pos,&uu,&uv,&vu,&vv);
// Now update BigInt variables
MatrixVecMul(&u,&v,uu,uv,vu,vv);
#if 1
// Make u,v positive
// Required only for Pornin's method
if(u.IsNegative()) {
u.Neg();
uu = -uu;
uv = -uv;
}
if(v.IsNegative()) {
v.Neg();
vu = -vu;
vv = -vv;
}
#endif
MatrixVecMul(&r,&s,uu,uv,vu,vv,&carryR,&carryS);
// Compute multiple of P to add to s and r to make them multiple of 2^62
uint64_t r0 = (r.bits64[0] * MM64) & MSK62;
uint64_t s0 = (s.bits64[0] * MM64) & MSK62;
r0_P.Mult(&_P,r0);
s0_P.Mult(&_P,s0);
carryR = r.AddCh(&r0_P,carryR);
carryS = s.AddCh(&s0_P,carryS);
// Right shift all variables by 62bits
shiftR(62, u.bits64);
shiftR(62, v.bits64);
shiftR(62, r.bits64, carryR);
shiftR(62, s.bits64, carryS);
//printf("U=%s\n",u.GetBase16().c_str());
//printf("V=%s\n",v.GetBase16().c_str());
//printf("R=%s\n",r.GetBase16().c_str());
//printf("S=%s\n",s.GetBase16().c_str());
totalCount++;
}
// u ends with +/-1
if(u.IsNegative()) {
u.Neg();
r.Neg();
}
if (!u.IsOne()) {
// No inverse
CLEAR();
return;
}
while(r.IsNegative())
r.Add(&_P);
while(r.IsGreaterOrEqual(&_P))
r.Sub(&_P);
Set(&r);
#endif
}
// ------------------------------------------------
void Int::ModExp(Int *e) {
Int base(this);
SetInt32(1);
uint32_t i = 0;
uint32_t nbBit = e->GetBitLength();
for(int i=0;i<(int)nbBit;i++) {
if (e->GetBit(i))
ModMul(&base);
base.ModMul(&base);
}
}
// ------------------------------------------------
void Int::ModMul(Int *a) {
Int p;
p.MontgomeryMult(a, this);
MontgomeryMult(&_R2, &p);
}
// ------------------------------------------------
void Int::ModSquare(Int *a) {
Int p;
p.MontgomeryMult(a, a);
MontgomeryMult(&_R2, &p);
}
// ------------------------------------------------
void Int::ModCube(Int *a) {
Int p;
Int p2;
p.MontgomeryMult(a, a);
p2.MontgomeryMult(&p, a);
MontgomeryMult(&_R3, &p2);
}
// ------------------------------------------------
bool Int::HasSqrt() {
// Euler's criterion
Int e(&_P);
Int a(this);
e.SubOne();
e.ShiftR(1);
a.ModExp(&e);
return a.IsOne();
}
// ------------------------------------------------
void Int::ModSqrt() {
if (_P.IsEven()) {
CLEAR();
return;
}
if (!HasSqrt()) {
CLEAR();
return;
}
if ((_P.bits64[0] & 3) == 3) {
Int e(&_P);
e.AddOne();
e.ShiftR(2);
ModExp(&e);
} else if ((_P.bits64[0] & 3) == 1) {
int nbBit = _P.GetBitLength();
// Tonelli Shanks
uint64_t e=0;
Int S(&_P);
S.SubOne();
while (S.IsEven()) {
S.ShiftR(1);
e++;
}
// Search smalest non-qresidue of P
Int q((uint64_t)1);
do {
q.AddOne();
} while (q.HasSqrt());
Int c(&q);
c.ModExp(&S);
Int t(this);
t.ModExp(&S);
Int r(this);
Int ex(&S);
ex.AddOne();
ex.ShiftR(1);
r.ModExp(&ex);
uint64_t M = e;
while (!t.IsOne()) {
Int t2(&t);
uint64_t i=0;
while (!t2.IsOne()) {
t2.ModSquare(&t2);
i++;
}
Int b(&c);
for(uint64_t j=0;j<M-i-1;j++)
b.ModSquare(&b);
M=i;
c.ModSquare(&b);
t.ModMul(&t,&c);
r.ModMul(&r,&b);
}
Set(&r);
}
}
// ------------------------------------------------
void Int::ModMul(Int *a, Int *b) {
Int p;
p.MontgomeryMult(a,b);
MontgomeryMult(&_R2,&p);
}
// ------------------------------------------------
Int* Int::GetFieldCharacteristic() {
return &_P;
}
// ------------------------------------------------
Int* Int::GetR() {
return &_R;
}
Int* Int::GetR2() {
return &_R2;
}
Int* Int::GetR3() {
return &_R3;
}
Int* Int::GetR4() {
return &_R4;
}
// ------------------------------------------------
void Int::SetupField(Int *n, Int *R, Int *R2, Int *R3, Int *R4) {
// Size in number of 32bit word
int nSize = n->GetSize();
// Last digit inversions (Newton's iteration)
{
int64_t x, t;
x = t = (int64_t)n->bits64[0];
x = x * (2 - t * x);
x = x * (2 - t * x);
x = x * (2 - t * x);
x = x * (2 - t * x);
x = x * (2 - t * x);
MM64 = (uint64_t)(-x);
MM32 = (uint32_t)MM64;
}
_P.Set(n);
// Size of Montgomery mult (64bits digit)
Msize = nSize/2;
// Compute few power of R
// R = 2^(64*Msize) mod n
Int Ri;
Ri.MontgomeryMult(&_ONE, &_ONE); // Ri = R^-1
_R.Set(&Ri); // R = R^-1
_R2.MontgomeryMult(&Ri, &_ONE); // R2 = R^-2
_R3.MontgomeryMult(&Ri, &Ri); // R3 = R^-3
_R4.MontgomeryMult(&_R3, &_ONE); // R4 = R^-4
_R.ModInv(); // R = R
_R2.ModInv(); // R2 = R^2
_R3.ModInv(); // R3 = R^3
_R4.ModInv(); // R4 = R^4
if (R)
R->Set(&_R);
if (R2)
R2->Set(&_R2);
if (R3)
R3->Set(&_R3);
if (R4)
R4->Set(&_R4);
}
// ------------------------------------------------
void Int::MontgomeryMult(Int *a) {
// Compute a*b*R^-1 (mod n), R=2^k (mod n), k = Msize*64
// a and b must be lower than n
// See SetupField()
Int t;
Int pr;
Int p;
uint64_t ML;
uint64_t c;
// i = 0
imm_umul(a->bits64, bits64[0], pr.bits64);
ML = pr.bits64[0] * MM64;
imm_umul(_P.bits64, ML, p.bits64);
c = pr.AddC(&p);
memcpy(t.bits64, pr.bits64 + 1, 8 * (NB64BLOCK - 1));
t.bits64[NB64BLOCK - 1] = c;
for (int i = 1; i < Msize; i++) {
imm_umul(a->bits64, bits64[i], pr.bits64);
ML = (pr.bits64[0] + t.bits64[0]) * MM64;
imm_umul(_P.bits64, ML, p.bits64);
c = pr.AddC(&p);
t.AddAndShift(&t, &pr, c);
}
p.Sub(&t,&_P);
if (p.IsPositive())
Set(&p);
else
Set(&t);
}
void Int::MontgomeryMult(Int *a, Int *b) {
// Compute a*b*R^-1 (mod n), R=2^k (mod n), k = Msize*64
// a and b must be lower than n
// See SetupField()
Int pr;
Int p;
uint64_t ML;
uint64_t c;
// i = 0
imm_umul(a->bits64, b->bits64[0], pr.bits64);
ML = pr.bits64[0] * MM64;
imm_umul(_P.bits64, ML, p.bits64);
c = pr.AddC(&p);
memcpy(bits64,pr.bits64 + 1,8*(NB64BLOCK-1));
bits64[NB64BLOCK-1] = c;
for (int i = 1; i < Msize; i++) {
imm_umul(a->bits64, b->bits64[i], pr.bits64);
ML = (pr.bits64[0] + bits64[0]) * MM64;
imm_umul(_P.bits64, ML, p.bits64);
c = pr.AddC(&p);
AddAndShift(this, &pr, c);
}
p.Sub(this, &_P);
if (p.IsPositive())
Set(&p);
}
// SecpK1 specific section -----------------------------------------------------------------------------
void Int::ModMulK1(Int *a, Int *b) {
#ifndef WIN64
#if (__GNUC__ > 7) || (__GNUC__ == 7 && (__GNUC_MINOR__ > 2))
unsigned char c;
#else
#warning "GCC lass than 7.3 detected, upgrade gcc to get best perfromance"
volatile unsigned char c;
#endif
#else
unsigned char c;
#endif
uint64_t ah, al;
uint64_t t[NB64BLOCK];
#if BISIZE==256
uint64_t r512[8];
r512[5] = 0;
r512[6] = 0;
r512[7] = 0;
#else
uint64_t r512[12];
r512[5] = 0;
r512[6] = 0;
r512[7] = 0;
r512[8] = 0;
r512[9] = 0;
r512[10] = 0;
r512[11] = 0;
#endif
// 256*256 multiplier
imm_umul(a->bits64, b->bits64[0], r512);
imm_umul(a->bits64, b->bits64[1], t);
c = _addcarry_u64(0, r512[1], t[0], r512 + 1);
c = _addcarry_u64(c, r512[2], t[1], r512 + 2);
c = _addcarry_u64(c, r512[3], t[2], r512 + 3);
c = _addcarry_u64(c, r512[4], t[3], r512 + 4);
c = _addcarry_u64(c, r512[5], t[4], r512 + 5);
imm_umul(a->bits64, b->bits64[2], t);
c = _addcarry_u64(0, r512[2], t[0], r512 + 2);
c = _addcarry_u64(c, r512[3], t[1], r512 + 3);
c = _addcarry_u64(c, r512[4], t[2], r512 + 4);
c = _addcarry_u64(c, r512[5], t[3], r512 + 5);
c = _addcarry_u64(c, r512[6], t[4], r512 + 6);
imm_umul(a->bits64, b->bits64[3], t);
c = _addcarry_u64(0, r512[3], t[0], r512 + 3);
c = _addcarry_u64(c, r512[4], t[1], r512 + 4);
c = _addcarry_u64(c, r512[5], t[2], r512 + 5);
c = _addcarry_u64(c, r512[6], t[3], r512 + 6);
c = _addcarry_u64(c, r512[7], t[4], r512 + 7);
// Reduce from 512 to 320
imm_umul(r512 + 4, 0x1000003D1ULL, t);
c = _addcarry_u64(0, r512[0], t[0], r512 + 0);
c = _addcarry_u64(c, r512[1], t[1], r512 + 1);
c = _addcarry_u64(c, r512[2], t[2], r512 + 2);
c = _addcarry_u64(c, r512[3], t[3], r512 + 3);
// Reduce from 320 to 256
// No overflow possible here t[4]+c<=0x1000003D1ULL
al = _umul128(t[4] + c, 0x1000003D1ULL, &ah);
c = _addcarry_u64(0, r512[0], al, bits64 + 0);
c = _addcarry_u64(c, r512[1], ah, bits64 + 1);
c = _addcarry_u64(c, r512[2], 0ULL, bits64 + 2);
c = _addcarry_u64(c, r512[3], 0ULL, bits64 + 3);
// Probability of carry here or that this>P is very very unlikely
bits64[4] = 0;
#if BISIZE==512
bits64[5] = 0;
bits64[6] = 0;
bits64[7] = 0;
bits64[8] = 0;
#endif
}
void Int::ModMulK1(Int *a) {
#ifndef WIN64
#if (__GNUC__ > 7) || (__GNUC__ == 7 && (__GNUC_MINOR__ > 2))
unsigned char c;
#else
#warning "GCC lass than 7.3 detected, upgrade gcc to get best perfromance"
volatile unsigned char c;
#endif
#else
unsigned char c;
#endif
uint64_t ah, al;
uint64_t t[NB64BLOCK];
#if BISIZE==256
uint64_t r512[8];
r512[5] = 0;
r512[6] = 0;
r512[7] = 0;
#else
uint64_t r512[12];
r512[5] = 0;
r512[6] = 0;
r512[7] = 0;
r512[8] = 0;
r512[9] = 0;
r512[10] = 0;
r512[11] = 0;
#endif
// 256*256 multiplier
imm_umul(a->bits64, bits64[0], r512);
imm_umul(a->bits64, bits64[1], t);
c = _addcarry_u64(0, r512[1], t[0], r512 + 1);
c = _addcarry_u64(c, r512[2], t[1], r512 + 2);
c = _addcarry_u64(c, r512[3], t[2], r512 + 3);
c = _addcarry_u64(c, r512[4], t[3], r512 + 4);
c = _addcarry_u64(c, r512[5], t[4], r512 + 5);
imm_umul(a->bits64, bits64[2], t);
c = _addcarry_u64(0, r512[2], t[0], r512 + 2);
c = _addcarry_u64(c, r512[3], t[1], r512 + 3);
c = _addcarry_u64(c, r512[4], t[2], r512 + 4);
c = _addcarry_u64(c, r512[5], t[3], r512 + 5);
c = _addcarry_u64(c, r512[6], t[4], r512 + 6);
imm_umul(a->bits64, bits64[3], t);
c = _addcarry_u64(0, r512[3], t[0], r512 + 3);
c = _addcarry_u64(c, r512[4], t[1], r512 + 4);